# What is a dimension?

1. Feb 11, 2004

### [ infinite ]

Hello all-

This is something that has been on my mind ever since I first learned about the fourth dimension and beyond, sometime back in fifth grade. This is simply one of those things that I never really 'got'.

What is a dimension? How does an n-th dimension (where n>3) exist? What exactly are the n-th dimensions (where n>3)? What is the evidence for their existence? How are dimensions relevant to scientific thought?

2. Feb 12, 2004

### HallsofIvy

A "dimension" is the number of "labels" (normally numbers but can be other things) necessary to identify something of interest.

If I am working with points on a given line or curve, I could choose any point on the line as a starting point and identify all other points by their distance (positive in one direction, negative in the other) from that point. I can identify each point by a single number- one dimension.

If I am working with points in the plane, surface of a sphere, or some other surface, I can set up a Cartesian coordinate system, or polar coordinates and, either way, identify each point by two numbers-two dimensional.

If I am working with points "in space", I will need three numbers- space is three dimensional.

If I am doing research on spheres, I might label each sphere by its center (I will need 3 numbers to label the center point) and its radius (one more number). That's a "four dimensional" problem.

Going to physics, the basic thing physicists work with is an "event"- something that happens at a specific point at a specific time. Identifying an event requires the 3 numbers to identify the point and one number to identify the time- four numbers, four dimensions. That's why physicists say they work in a "four dimensional space-time continuum".

On the other hand, if I am working on thermodynamics, with a gas of, say N molecules, I might wish to identify the position (3 numbers) and the momentum vector (another 3 numbers) of each molecule as well as the time. I would be working in "6N+1" dimensional space.

3. Feb 12, 2004

### pmb_phy

I wanted to address this question once and for all some time back so I created this web page. See
http://www.geocities.com/physics_world/ma/coord_system.htm

4. Feb 12, 2004

### [ infinite ]

Thanks for the reply, it was really comprehensive and made things much more lucid. Also thanks for the site pmb_phy.